(CNN) -- Sen. Barack Obama Wednesday challenged Sen. Hillary Clinton's claim that she was the best candidate to take on Sen. John McCain in the fall.

"If the suggestion is somehow that ... she's going to have a better record than I have and will be better able to withstand Republican attacks, I think that's an issue that should be tested," the Illinois Democrat told reporters Wednesday.

"I think that I am in a much stronger position to run against the Republicans than she is, otherwise I wouldn't be running for president," Obama said.

The argument over who would be the best candidate to take on McCain will likely dominate the Democratic race over the next seven weeks as the campaigns turn their attention to the Pennsylvania primary on April 22.

Clinton won in Texas, Ohio, and Rhode Island, while Obama won Vermont. Many of her supporters had said she had to win both Texas and Ohio to continue to challenge Obama for her party's nomination. Watch a preview of the fight ahead »

The next two Democratic contests are the Wyoming caucuses on Saturday and the Mississippi primary on March 11.

"People who voted a month ago didn't know who the Republican nominee was going to be. They didn't perhaps factor in that it will be about national security because, indeed, with Senator McCain, that's what it will be about," Clinton told CNN Wednesday.Watch Clinton say she can beat McCain »

"I have a lifetime of experience. Senator McCain has a lifetime of experience. Senator Obama's campaign is about one speech he made in 2002," she said, referring to the Illinois Democrat's speech in which he announced his opposition to the then-pending invasion of Iraq.

But Obama said the voters had rejected Clinton's argument that she was the more experienced candidate.

"One of the things that I hope people start asking is what exactly is this foreign experience that she's claiming," Obama said. "I have not seen any evidence that she is better equipped to handle a crisis."

"If the only criteria is longevity in Washington, then she's certainly not going to beat John McCain on that," he said.

Despite the heated back-and-forth over the last few months, Clinton Wednesday hinted that she would be open to a Clinton-Obama ticket in the fall.

"Well, that may, you know, be where this is headed," Clinton told CBS Wednesday. "But, of course, we have to decide who's on top of the ticket, and I think that the people of Ohio very clearly said that it should be me."

Obamahad built up a lead in the delegate count before Tuesday. He leads Clinton in delegates 1,520 to 1,424, CNN estimates. A candidate needs 2,025 national convention delegates to win the Democratic presidential nomination.

Obama said Wednesday the results do not fundamentally change the race.

"It goes to Wyoming and Mississippi, which we've got coming up this week, and then on to Pennsylvania and a series of other states -- North Carolina, Kentucky, Indiana," he told CNN Wednesday. "We are confident that after last night ... we end up emerging with essentially the same delegate count that we had going in and feel confident that we're going to be able to go on to the nomination." Watch Obama say what he's focused on now »

Delegate-rich Texas and Ohio were considered must-wins to keep Clinton's campaign alive.